So as I understood, the clearing account will be a place to put all the revenues and costs on it, before bank statement reconciliation.

But, what does make the clearing account journal having the ability to reconcile the already recorded payments, with bank statement line ? is there a parameter on journal or account creation I should put to give this ability ?

This does not work in standard. If you do not have too many currency, you can create a clearing account and the related journal. When you register the payment, you register it with the clearing account payment method. Then, when the bank statement arrives, you will reconcile the bank entry with the clearing entry.

Import only unpaid invoices so the system automatically loads the accounting entries, and create automatically the reconciliation couterpart. But, when the bank statement line, refers to a payement already recorded on our accounting book, there is no reconciliation with the existing Payement.

I want to reconcile the already recorded payement on my accounting book ( openerp accounting system ), with the already existing payment on my openerp accounting system.

Opernerp v7 reconcile just the payments existing on the bank statement, and non existing on our openerp accounting system, so for me it's just normal reconciliation process. and not an efficient bank statement reconciliation, mainly when the reconciliation button stays RED.